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Tautological one-form. In mathematics, the tautological one-form is a special 1-form defined on the cotangent bundle of a manifold In physics, it is used to create a correspondence between the velocity of a point in a mechanical system and its momentum, thus providing a bridge between Lagrangian mechanics and Hamiltonian mechanics (on the ...
1040. As of the 2018 tax year, Form 1040, U.S. Individual Income Tax Return, is the only form used for personal (individual) federal income tax returns filed with the IRS. In prior years, it had been one of three forms (1040 [the "Long Form"], 1040A [the "Short Form"] and 1040EZ - see below for explanations of each) used for such returns.
In mathematics, Liouville's theorem, proved by Joseph Liouville in 1850, [1] is a rigidity theorem about conformal mappings in Euclidean space. It states that every smooth conformal mapping on a domain of Rn, where n > 2, can be expressed as a composition of translations, similarities, orthogonal transformations and inversions: they are Möbius ...
Sturm–Liouville theory. In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form: for given functions , and , together with some boundary conditions at extreme values of . The goals of a given Sturm–Liouville problem are: To find the λ for which there exists a non ...
In mathematics, Liouville's formula, also known as the Abel–Jacobi–Liouville identity, is an equation that expresses the determinant of a square-matrix solution of a first-order system of homogeneous linear differential equations in terms of the sum of the diagonal coefficients of the system. The formula is named after the French ...
The government of Louisville, Kentucky, headquartered at Louisville City Hall in Downtown Louisville, is organized under Chapter 67C of the Kentucky Revised Statutes as a First-Class city in the state of Kentucky. Created after the merger of the governments of Louisville, Kentucky and Jefferson County, Kentucky, the city/county government is ...
U.S. Route 31W. U.S. Route 31W ( US 31W) is the westernmost of two parallel routes for U.S. Route 31 from Nashville, Tennessee to Louisville, Kentucky . Tennessee State Route 41 (SR 41) is its unsigned companion route in Tennessee. During the December 2021 tornado outbreak, an EF3 tornado devastated stretches of US 31W in Bowling Green, Kentucky.
Louisville [b] is the most populous city in the Commonwealth of Kentucky, sixth-most populous city in the Southeast, and the 27th-most-populous city in the United States. [a] [11] By land area, it is the country's 24th-largest city, although by population density, it is the 265th most dense city. [c] [12] Louisville is the historical county ...